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Simplifying 3x3 + -9x2 + 5x = 0 Reorder the terms: 5x + -9x2 + 3x3 = 0 Solving 5x + -9x2 + 3x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(5 + -9x + 3x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(5 + -9x + 3x2)' equal to zero and attempt to solve: Simplifying 5 + -9x + 3x2 = 0 Solving 5 + -9x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + -3x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -3x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -3x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -3x + x2 = 0 + -1.666666667 -3x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -3x + x2 = -1.666666667 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -1.666666667 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -1.666666667 + 2.25 Combine like terms: -1.666666667 + 2.25 = 0.583333333 2.25 + -3x + x2 = 0.583333333 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 0.583333333 Calculate the square root of the right side: 0.763762616 Break this problem into two subproblems by setting (x + -1.5) equal to 0.763762616 and -0.763762616.Subproblem 1
x + -1.5 = 0.763762616 Simplifying x + -1.5 = 0.763762616 Reorder the terms: -1.5 + x = 0.763762616 Solving -1.5 + x = 0.763762616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 0.763762616 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 0.763762616 + 1.5 x = 0.763762616 + 1.5 Combine like terms: 0.763762616 + 1.5 = 2.263762616 x = 2.263762616 Simplifying x = 2.263762616Subproblem 2
x + -1.5 = -0.763762616 Simplifying x + -1.5 = -0.763762616 Reorder the terms: -1.5 + x = -0.763762616 Solving -1.5 + x = -0.763762616 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -0.763762616 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -0.763762616 + 1.5 x = -0.763762616 + 1.5 Combine like terms: -0.763762616 + 1.5 = 0.736237384 x = 0.736237384 Simplifying x = 0.736237384Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.263762616, 0.736237384}Solution
x = {0, 2.263762616, 0.736237384}
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